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Simplifying -2x2 + -9 + 12x + 18x2 + -15x = 0 Reorder the terms: -9 + 12x + -15x + -2x2 + 18x2 = 0 Combine like terms: 12x + -15x = -3x -9 + -3x + -2x2 + 18x2 = 0 Combine like terms: -2x2 + 18x2 = 16x2 -9 + -3x + 16x2 = 0 Solving -9 + -3x + 16x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.5625 + -0.1875x + x2 = 0 Move the constant term to the right: Add '0.5625' to each side of the equation. -0.5625 + -0.1875x + 0.5625 + x2 = 0 + 0.5625 Reorder the terms: -0.5625 + 0.5625 + -0.1875x + x2 = 0 + 0.5625 Combine like terms: -0.5625 + 0.5625 = 0.0000 0.0000 + -0.1875x + x2 = 0 + 0.5625 -0.1875x + x2 = 0 + 0.5625 Combine like terms: 0 + 0.5625 = 0.5625 -0.1875x + x2 = 0.5625 The x term is -0.1875x. Take half its coefficient (-0.09375). Square it (0.0087890625) and add it to both sides. Add '0.0087890625' to each side of the equation. -0.1875x + 0.0087890625 + x2 = 0.5625 + 0.0087890625 Reorder the terms: 0.0087890625 + -0.1875x + x2 = 0.5625 + 0.0087890625 Combine like terms: 0.5625 + 0.0087890625 = 0.5712890625 0.0087890625 + -0.1875x + x2 = 0.5712890625 Factor a perfect square on the left side: (x + -0.09375)(x + -0.09375) = 0.5712890625 Calculate the square root of the right side: 0.755836664 Break this problem into two subproblems by setting (x + -0.09375) equal to 0.755836664 and -0.755836664.Subproblem 1
x + -0.09375 = 0.755836664 Simplifying x + -0.09375 = 0.755836664 Reorder the terms: -0.09375 + x = 0.755836664 Solving -0.09375 + x = 0.755836664 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.09375' to each side of the equation. -0.09375 + 0.09375 + x = 0.755836664 + 0.09375 Combine like terms: -0.09375 + 0.09375 = 0.00000 0.00000 + x = 0.755836664 + 0.09375 x = 0.755836664 + 0.09375 Combine like terms: 0.755836664 + 0.09375 = 0.849586664 x = 0.849586664 Simplifying x = 0.849586664Subproblem 2
x + -0.09375 = -0.755836664 Simplifying x + -0.09375 = -0.755836664 Reorder the terms: -0.09375 + x = -0.755836664 Solving -0.09375 + x = -0.755836664 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.09375' to each side of the equation. -0.09375 + 0.09375 + x = -0.755836664 + 0.09375 Combine like terms: -0.09375 + 0.09375 = 0.00000 0.00000 + x = -0.755836664 + 0.09375 x = -0.755836664 + 0.09375 Combine like terms: -0.755836664 + 0.09375 = -0.662086664 x = -0.662086664 Simplifying x = -0.662086664Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.849586664, -0.662086664}
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